Reduction of circuit depth by mapping qubit-based quantum gates to a qudit basis

TL;DR

This paper introduces a scalable method for mapping qubit-based quantum gates to a qudit basis, significantly reducing circuit depth for large systems by optimizing gate implementation and control.

Contribution

It presents a systematic approach to implement universal and multiply controlled gates in a qudit basis with minimal ancilla use, improving scalability and efficiency.

Findings

Qudit-based circuits show dramatically reduced depth compared to qubit circuits as system size increases.

The method minimizes the use of ancilla levels in implementing gates.

Multiplying controlled gates are key to the depth reduction in qudit systems.

Abstract

We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as well as the NOT gate and multiply-controlled-Z gates, we describe a systematic approach to identifying the set of U(2) rotations required to implement each gate for any qudit of size N and with minimal use of an ancilla level. The qudit gates are analyzed in terms of the total rotation count and gate depth as the system scales with D. We apply the qudit-basis to Grover's Algorithm and compare the circuit depth vs. system size to a qubit-based circuit. The results show that there is a dramatic reduction in circuit depth as the size of the system increases for the qudit circuit compared to qubit circuit. In particular, multiply controlled gates are the driving factor in the reduction of circuit complexity for qudit-based system scales with D.